Logistic

A practical question in species surveillance is “How much search effort is required for detection?”. This can be quantified under controlled conditions where the number and location of target species are known and participants are recruited to see how success rate varies.
Let’s use an example of an easter egg hunt where the adult (the researcher) wants to quantify how much effort it takes a child (the participant) to find an easter egg.

For a given species, a simple mortality response to environmental conditions can represented with the probabilistic outcome (death), which occurs with probabilty (p). This simple process is know as a Bernoulli random variable.
A motivating example is how a pest responds to increasing doses of a pesticide. Invertebrate pests cause 10-20% of yield losses in modern food systems. While cultural practices such as crop rotatation and biological control through beneficial insects increasingly form a core component of effective and sustainable management, pesticides remain a widely used tool.

For a given species, a simple mortality response to environmental conditions can represented with the probabilistic outcome (death), which occurs with probabilty (p). This simple process is know as a Bernoulli random variable.
A motivating example is how a pest responds to increasing doses of a pesticide. Invertebrate pests cause 10-20% of yield losses in modern food systems. While cultural practices such as crop rotatation and biological control through beneficial insects increasingly form a core component of effective and sustainable management, pesticides remain a widely used tool.

What if a growing population gets eaten by another population?
In a previous post I showed why we might expect a population to grow exponentially when not resource limited. We then extended this to the case where a population reaches some carrying capacity (using a simple and non-mechanistic logistic function).
But population growth can also be curtailed through interactions with another species population, such as a predator. In my area of study, we deal with a lot of herbivorous pests of agricultural systems.

Let’s derive some more population growth functions!
The logistic population growth function In a previous post we derived a function for population growth based on the vital rates of reproduction and mortality. We assumed that the growth rate was constant with respect to the number of individuals in the population or (\frac{dt}{dN} = rN). This led to the unrealistic prediction that populations will grow indefinitely. Of course, populations will eventually run into resource problems (e.